EAN: 9783319609393

ADVANCED COURSES IN MATHEMATICS - CRM BARCELONA...

This volume presents the lecture notes from the authors' three summer courses offered during
the program Automorphisms of Free Groups: Geometry  Topology  and Dynamics  held at the Centre
de Recerca Matemàtica (CRM) in Bellaterra  Spain. The first two chapters present the basic
tools needed  from formal language theory (regular and context-free languages  automata 
rewriting systems  transducers  etc) and emphasize their connections to group theory  mostly
relating to free and virtually-free groups. The material covered is sufficient to present full
proofs of many of the existing interesting characterizations of virtually-free groups. In turn
the last chapter comprehensively describes Bonahon's construction of Thurston's
compactification of Teichmüller space in terms of geodesic currents on surfaces. It also
includes several intriguing extensions of the notion of geodesic current to various other  more
general settings.

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